Conformality or confinement: (Ir)relevance of topological excitations

The non-perurbative dynamics of QCD-like and chiral gauge theories has remained largely elusive despite much effort. Recently, novel techniques [such as twisted partition functions and center stabilizing double trace deformations] which allow us to continuously connect the physics of these gauge theories on R4 to small (non-thermal) S1 x R3 are found. In most cases the physics of small S1 is analytically tractable and provides much inside to the dynamics. Mass gap and confinement are typically caused by a new class of non-selfdual topological excitations referred to as magnetic bions [a class different from the well-known monopoles and instantons], and in some cases chiral symmetry breaking is probed by topological disorder operators. In this talk I will overview the recent progress. Then, I will discuss why an asymptotically free gauge theory can flow either to confinement or conformality. This answer is typically tied with relevance versus irrelevance of magnetic bions.